A yankin na Prism tushe, daga triangular zuwa polygonal

Sauran prisms daban-daban daga juna. A lokaci guda suna da yawa a cikin na kowa. Don samun da yankin na Prism tushe, bukatar fahimtar abin da irin shi.

Janar ka'idar

Prism ne wani polyhedron, da tarnaƙi na wanda suna da wani nau'i na parallelogram. A wannan yanayin, karkashi iya zama wani polytope - daga alwatika ga n-gon. Cikinsa da Prism tushe ne ko da yaushe daidai da juna. Wannan bai shafi bangarorin - su iya bambanta ƙwarai a cikin size.

A warware matsaloli ci karo da ba kawai da yankin na Prism tushe. Yana iya bukatar ilmi daga gefen surface, wato, dukan fuskoki da cewa ba su da kwasfansu. Complete surface yana zama cikin ƙungiyar na duk fuskoki da cewa yin up da Prism.

Wani lokaci tsawo bayyana a cikin matsaloli. Shi ne perpendicular da tushe. Diagonal na polyhedron ne a kashi cewa ya haɗu da wani biyu vertices nau'i-nau'i ba na zuwa wannan fuska.

Ya kamata a lura da cewa yankin na tushe na da hakkin Prism ko karkata mai zaman kanta da kwana tsakanin su, kuma a kaikaice fuskoki. Idan suna da wannan siffar a saman da kasa fuskokin, su yankunan su ne daidai.

triangular Prism

Shi ne a gindi daga cikin adadi da ciwon uku vertices, cewa shi ne mai alwatika. Ya aka sani ya zama daban-daban. Idan alwatika ne rectangular, shi ne isa zuwa tuna cewa wurin da aka ayyana da kafafu da rabi na aiki.

A ilmin lissafi magana ne kamar haka: S = ½ dari.

Don samun fannin wani triangular Prism tushe a general form, amfani dabara Heron da kuma daya a cikin abin da hannun da aka dauka rabin tsayinta da za'ayi a cikinta.

A farko dabara ne da za a rubuta kamar: S = √ (p (p-kyau) (p-c) (p-c)). semiperimeter (p) ne ba a cikin rikodin, cewa shi ne Naira Miliyan Xari da uku tarnaƙi, raba ta biyu.

Na biyu: S = ½ _kuma n * a.

Idan da ake bukata domin koyi sawun triangular Prism wanda shi ne daidai, sa'an nan da alwatika ne equilateral. Ga shi yana da dabara: S = ¼ da kuma ² * √3.

quadrangular Prism

Its tushe ne wani sananne quadrangles. Wannan zai iya zama murabba'i mai dari, ko da wani square, rhombus, ko wani akwatin. A kowane hali, domin yin lissafi da yankin na Prism tushe, shi zai bukatar nasu dabara.

Idan substrate - a murabba'i mai dari, ta yankin da aka ayyana a matsayin: S = AV, inda A da B - na murabba'i mai dari.

Idan ya zo ga wani quadrangular Prism, da Prism tushe dace yanki da aka lasafta ta dabara domin a square. Saboda cewa abin da shi dai itace za a kwance a kasa. Kuma S = ^2.

A cikin akwati inda tushe - shi ne mai akwatin, shi zai bukatar irin wannan lissafi: S = a * n _wani. Sai ya faru da cewa akwatin gefen kuma suna daya daga cikin sasanninta. Sa'an nan, ya lissafta da tsawo na da bukatar amfani da ƙarin dabara: N _mai = b * zunubi A. Bugu da ƙari, cikin kwana A ne m zuwa gefen "b" da kuma tsawo n _{da kuma} daura da wannan kusurwa.

Idan tushe na Prism ne rhombus, sa'an nan sanin da yankin zai bukata guda dabara kamar cewa da wani parallelogram (as shi ne ya batu). Amma daya kuma iya amfani da irin wannan: S = ½ d ₁ d _2. A nan, d ₁ da d ₂ - biyu diagonals na wani rhombus.

Pentagonal Prism

Wannan harka unshi da bazuwar daga cikin polygon cikin triangles wanda yankunan su ne sauki don koyi. Ko da yake shi ya faru da cewa Figures iya zama daban-daban yawan vertices.

Tun da Prism tushe - na yau da kullum Pentagon, shi za a iya raba biyar equilateral alwatika. Sa'an nan Prism tushe yanki daidaita da yankin na alwatika (ga sama dabara za a iya) ta tara da biyar.

Regular kyakkyawan Prism

Bisa ga manufa da aka bayyana a pentagonal Prism, shi ne zai yiwu ya karya heksagon tushe 6 equilateral triangles. Formula sawun irin Prism kama da na baya. Kawai a cikin shi wani equilateral alwatika yanki ya kamata a yawaita da shida.

Duba dabara ne kamar haka: S = 3/2 da kuma ² * √3.

ayyuka

Number 1. Dana dama mike rectangular Prism. Its diagonal daidaita zuwa 22 cm, da polyhedron tsawo - 14 cm lissafi Prism tushe yankin da kuma dukan surface ..

Rarrabẽwa. Prism tushe ne square, amma jam'iyyar ba a sani. Yana yiwuwa a sami darajar da diagonal da wani square (x), wanda ake dangantawa da diagonal Prism (d) da kuma rufinta (n). x ² = d ² - N ^2. A daya hannun, wannan kashi na "x" ne hypotenuse na alwatika wanda kafafu daidai suke da da gefen square. Watau x ² = wata ² + ^2. Kamar haka dai itace cewa a ² = (d ² - n ²⁾ / 2.

D canza lambar 22, da kuma "n" da aka maye gurbinsu da darajar - 14, shi dai itace cewa gefe na square ne daidai da 12 cm Yanzu kawai koyi sawun: 12 * 12 = 144 cm ^{2 ..}

Don samun fannin dukan surface, shi wajibi ne don kwanta darajar sau biyu tushe da hudu da square gefe. A karshen ne mai sauki samu da dabara domin murabba'i mai dari: ninka da tsawo da kuma zuwa ga tushe na polyhedron. Watau 14 da kuma 12, wannan adadin zai zama daidai da 168 cm ^2. A duka yankin na Prism surface ne 960 ^cm2.

Amsa. A yankin na Prism tushe ne daidai to 144 cm ^2. Dukan surface - 960 ^cm2.

Number 2. Dan yau da kullum triangular Prism. A tushe ne alwatika tare da wani gefe na 6 cm Wannan diagonal gefen fuska ne 10 cm square lissafi: .. A tushe da kuma a gefen surface.

Rarrabẽwa. Tun da Prism daidai ne, to, karkashi ne equilateral alwatika. Saboda haka, wani yanki 6 ne daidaita da Squared, yawaita da ¼ da square tushen na 3. A sauki lissafi ba sakamakon: 9√3 ^cm2. Wannan yanki na daya tushe na Prism.

All gefen fuskoki ne m da kuma wakiltar rectangles tare da bangarorin 6, kuma 10 cm. Domin yin lissafi su yankin da isasshen ninka da lambobi. Sa'an nan riɓaɓɓanya su ta uku, saboda gefen fuskantar a cikin Prism sosai. Sa'an nan gefen surface na ciwo yanki ne 180 cm ^2.

Amsa. Square: substrate - 9√3 ^cm2, gefen surface wani Prism - 180 cm ^2.